Question 127679: Solve for x:
a) (log base2 x)^2-(logbase2 x^2)=0
b) log base2(logbasex 64)=1
c) log base5(5x+2)=1/2 logbase5 49+logbase5 16
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Solve for x:
a) (log base2 x)^2-(logbase2 x^2)=0
(log base2 x)^2 - 2(logbase2 x) = 0
Factor:
(log base2 x)(log base2 x -2) = 0
One of those factors must be zero:
If log base2 x = 0, then 2^0=x and x = 1
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If log base2 x-2 = 0, then log base2 x = 2 and x = 2^2 = 4
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b) log base2(log basex 64)=1
log basex 64 = 2^1
x^2 = 64
x = 8
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c) log base5(5x+2)=1/2 logbase5 49+logbase5 16
log base5(5x+2) = logbase5 7 + logbase5 16
log base5(5x+2) = logbase5 (7*16)
5x+2 = 112
5x = 110
x = 22
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Cheers,
stan H.
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